An angle is a geometric figure consisting of two lines, rays, or line segments with a common endpoint:

The endpoint of the angle is called the vertex. In the angle pictured above, the vertex is point A. The angle can be called either angle CAB or angle BAC. When naming an angle in this way, the only rule is that the vertex must be the middle “initial” of the angle. The SAT will also refer to angles using symbols:

Angles are measured in degrees, sometimes denoted by the symbol º. There are 360º in a complete rotation around a point; a circle therefore has 360º. There are some other ways to measure angles, such as radians. You may not have learned about radians in high school. Well, don’t worry about them. For the SAT, you only have to be familiar with degrees.

Take two intersecting lines. The intersection of these lines produces four angles.

From the diagram below, you should see that the four angles together encompass one full revolution around the two lines’ point of intersection. Therefore, the four angles produced by two intersection lines total 360º; angle a + b + c + d = 360º.

There are different types of angles, categorized by the number of degrees they have.

An angle with a measure of 0º is called a zero angle. If this is hard to visualize, consider two lines that form some angle greater than 0º. Then picture one of the lines rotating toward the other until they both fall on the same line. The angle they create has been shrunk from its original measure to 0º, forming a zero angle:

An angle with a measure of 90º is called a right angle. Notice that a right angle is symbolized with a square drawn in the corner of the angle. Whenever you see that little square, you know that you are dealing with a right angle.

Right angles often have special properties. We’ll take a look at these properties later on. For now, it’s enough to say that while taking the SAT, you should be on the lookout for the little square that denotes a right angle.

An angle with a measure of 180º is called a straight angle. It looks just like a line. Don’t confuse straight angles with zero angles, which look like a single ray.

Another way to classify an angle is by whether its measure is greater or less than 90º. If an angle measures less than 90º, it’s called an acute angle. If it measures more than 90º, it’s called an obtuse angle. Right angles are neither acute nor obtuse. They’re just right.

In the picture below, is acute while is obtuse.

Special names are given to pairs of angles whose sums equal either 90º or 180º. Angles whose sum is 90º are called complementary angles. If two angles sum to 180º, they’re called supplementary angles.

In the picture above and are complementary, since together they make up a right angle. Angle and are supplementary, since they make up a straight line.

On the SAT, you will often have to use the rules of complementary and supplementary angles to figure out the degree measure of an angle. For instance, let’s say you are given the following diagram and are told that AC is a line:

The picture tells you that is 113º, but how many degrees is Well, since you know that AC is a line, you know that is a straight angle and equals 180º. You also know that and are supplementary angles that add up to 180º. Therefore, to find out the value of you can simply take 180º and subtract 113º, which tells you that = 67º.

When two lines (or line segments) intersect, the angles that lie opposite each other, called vertical angles, are always equal.

Angle and are vertical angles and are therefore equal to each other. Angle and are also vertical (and equal) angles. This is very important knowledge for the SAT. At some point during the test, you will likely be asked to figure out the degree of an angle, and knowing this rule will help you immensely.

Pairs of lines that never intersect are called parallel lines.

On the SAT, never assume that two lines are parallel just because they look as if they are. If the lines are parallel, the SAT will tell you.

Lines (or segments) are called perpendicular if their intersection forms a right angle. Notice that if one of the angles formed by the intersection of two lines or segments is a right angle, then all four angles created will also be right angles (incidentally illustrating our point that the four angles formed by two intersecting lines will equal 360º, since 90º + 90º + 90º + 90º = 360º).

As with parallel lines, don’t assume that lines on the SAT are perpendicular unless the SAT states that they are. The SAT will alert you to perpendicular lines either by stating that two lines are perpendicular or by using the little box to indicate that the angles are 90º.

Also, you should note that if you see two lines that intersect and you know that the two lines form one right angle, but you don’t explicitly know the value of the other three angles, you still know that the two lines are perpendicular and that all four angles equal 90º. Think about it. If you know that one angle is equal to 90º, then you can use the rules of supplementary angles to prove that all angles are equal to 90º.

When two parallel lines are cut by a third straight line, the third line, known as a transversal, will intersect with each of the parallel lines. The eight angles created by these two intersections have special relationships with one another.

Angles 1, 4, 5, and 8 are all equal to each other. So are angles 2, 3, 6, and 7. Also, the sums of any two adjacent angles, such as 1 and 2 or 7 and 8 equal 180º. From these rules, you can make justified claims about seemingly unrelated angles. For example, since angles 1 and 2 sum to 180º—and since angle 2 and 7 are equal—the sum of angle 1 and 7 also equals 180º. The SAT likes to test this topic. When you see parallel lines cut by a transversal, you should immediately know how the angles are related. If you just know that angle 2 and angle 7 are equal, you will be able to answer the question a lot more quickly than if you have to work out the question by using the rules of supplementary and complementary angles.